Classification of topological insulators and superconductors in three spatial dimensions
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In this paper, the authors systematically studied topological phases of insulators and superconductors in three dimensions and showed that there exist topologically nontrivial (3D) topologically nonsmooth topological insulators in five out of ten symmetry classes introduced in the context of random matrix theory.Abstract:
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced ${\mathbb{Z}}_{2}$ topological insulator in the symplectic (or spin-orbit) symmetry class. We show that there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in three dimensions, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. Three of the above five topologically nontrivial phases can be realized as time-reversal invariant superconductors. In these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a two-dimensional surface, they support a number (which may be an arbitrary nonvanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin-rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations of the Hamiltonian that preserve the characteristic discrete symmetries, including disorder. In particular, these surface modes completely evade Anderson localization from random impurities. These topological phases can be thought of as three-dimensional analogs of well-known paired topological phases in two spatial dimensions such as the spinless chiral $({p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y})$-wave superconductor (or Moore-Read Pfaffian state). In the corresponding topologically nontrivial (analogous to ``weak pairing'') and topologically trivial (analogous to ``strong pairing'') 3D phases, the wave functions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the superconducting phases with nonvanishing winding number possess nontrivial topological ground-state degeneracies.read more
Citations
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Topological insulators and superconductors
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TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
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Topological Photonics
Tomoki Ozawa,Hannah M. Price,Alberto Amo,Nathan Goldman,Mohammad Hafezi,Ling Lu,Mikael C. Rechtsman,David Schuster,Jonathan Simon,Oded Zilberberg,Iacopo Carusotto +10 more
TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
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A tunable topological insulator in the spin helical Dirac transport regime
David Hsieh,Yuqi Xia,Dong Qian,Lewis Wray,Jan Hugo Dil,Jan Hugo Dil,Fabian Meier,Fabian Meier,Jürg Osterwalder,Luc Patthey,Joseph Checkelsky,Nai Phuan Ong,Alexei V. Fedorov,Hsin Lin,Arun Bansil,D. Grauer,Yew San Hor,Robert J. Cava,M. Z. Hasan +18 more
TL;DR: The results reveal a spin-momentum locked Dirac cone carrying a non-trivial Berry’s phase that is nearly 100 per cent spin-polarized, which exhibits a tunable topological fermion density in the vicinity of the Kramers point and can be driven to the long-sought topological spin transport regime.
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Topological insulators and superconductors: Tenfold way and dimensional hierarchy
TL;DR: In this paper, the authors constructed representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians.
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